This invention relates generally to the field of optical lithography, and more particularly, to a method for incorporating long-range flare effects in an Optical Proximity Correction (OPC) software tool for use in a model-based optical lithography simulation, to provide a fast and accurate correction of the device shapes in a photo-mask.
The optical micro-lithography process in semiconductor fabrication, also known as the photolithography process, consists of duplicating desired circuit patterns onto semiconductor wafers for an overall desired circuit performance. The desired circuit patterns are typically represented as opaque, complete and semi-transparent regions on a template commonly referred to as a photomask. In optical micro-lithography, patterns on the photo-mask template are projected onto the photo-resist coated wafer by way of optical imaging through an exposure system.
The continuous advancement of VLSI chip manufacturing technology to meet Moore's law of shrinking device dimensions in geometric progression has spurred the development of Resolution Enhancement Techniques (RET) and Optical Proximity Correction (OPC) methodologies in optical microlithography. The latter is the method of choice for chip manufacturers for the foreseeable future due to its high volume yield in manufacturing and past history of success. However, the ever shrinking device dimensions combined with the desire to enhance circuit performance in the deep sub-wavelength domain require complex OPC methodologies to ensure the fidelity of mask patterns on the printed wafer.
Current OPC algorithms pre-correct the mask shapes by segmenting the shape edges and shifting the position of the segments by small amounts. In the current state of the art, Model-Based OPC (MBOPC) software emulates the physical and optical effects that are mostly responsible for the non-fidelity of mask shapes printed on the wafer, as will be described hereinafter with reference to FIG. 1. In the correction phase of MBOPC, the mask shapes are iteratively modified so that the shapes printed on the wafer match the desired shape as closely as possible. This method automatically deforms existing mask shapes to achieve the target dimensions on the wafer.
The aforementioned methodology is illustrated in FIG. 1. In the current state of the art, an input mask layout 101 and a target image 105 are provided. The mask shapes are divided into segments 102, where each segment is provided with a self-contained evaluation point. The optical and the resist image are then evaluated at evaluation points 103. The images at each of the evaluation points are then checked against the tolerance of the target image 104. If the image does not remain within tolerance the segment is iteratively moved forward or backward 106 until all segments reside within an accepted tolerance. Eventually, the final corrected mask layout is outputted 107.
The core of the method herein described is a computer simulation program that accurately predicts the printed dimension of the shape on the wafer within the appropriate optical and physical parameters, and the original dimension of the shape on the mask, as illustrated in FIG. 2. The success of the model-based OPC depends on using a highly accurate simulator to predict the lithographic processing effects on selected points on the mask shapes which, ultimately, are printed on the wafer. Based on the simulation, an integrated circuit layout modeler determines the overall printed image on the wafer by interpolating selected simulated points.
Aerial image simulators which compute the images generated by optical projection systems have proven to be a valuable tool for analyzing and improving the state of the art of optical lithography systems for the fabrication of integrated circuits. These simulators have found wide application in advanced mask designs, such as phase shifting mask (PSM) design, optical proximity correction (OPC), and design of projection optics. Modeling aerial images is a crucial component of semiconductor manufacturing. Since present lithographic tools employ partially coherent illumination, such modeling is computationally intensive for all but the most elementary patterns. The aerial image generated by the mask, i.e., the light intensity of an optical projection system image plane, is a critically important parameter in micro-lithography for governing how well a developed photo-resist structure replicates a mask design and which, generally, needs to be computed to an accuracy of better than 1%.
In prior art MBOPC tools, the physical effects simulated include only the diffraction of light in the presence of low order aberrations which limit the accuracy of the predictions. One significant effect not currently included is the scattered light which affects the exposure over long distances on the wafer. Such long-range optical effects are generally referred to as “flare” in the literature. Given the current extremely tight requirements on Across-Chip-Line-Width-Variation (ACLV), flare effects need to be included. Also, in some cases, novel RET methods such as alternating Phase Shifting Masks (Alt-PSM) can exacerbate the problem by requiring dual exposure. The problem is even more pronounced in bright field masks that are used in printing critical levels which control the ultimate performance of the circuit, such as gate and diffusion levels.
Referring now to FIG. 2, there is described how the prior art methodology simulates the image intensity at a given point due to optical effects. The input to this methodology 201 is a mask layout and a pre-defined point 251, and a set of process parameters 202 including the light wavelength λ, source parameters, such as σ1 and σ2, the numerical aperture NA and Zernike parameters defining the lens aberrations. In the next step 203, an interaction region 252 around the point is considered, as are all the mask shapes or portions thereof within the box. The interaction region is a square box having dimensions of a few microns. The size of the box is determined by the computational speed versus accuracy tradeoff. Step 204 computes the SOCS (Sum of Coherent Systems) kernels, which description is given hereinafter. In step 205, the shapes obtained from step 203 are convolved with the kernels obtained in step 204. The kernel values are summed up in step 206 and stored in a discrete two dimensional array. The particular image intensity value is determined in step 207 from the summed values obtained by interpolating the values in the array.
Accuracy is of critical importance to the computation of calibrated optical or resist models. The accuracy in the simulation of wafer shapes is necessary to gain a better understanding and provide an improved evaluation of the OPC methodologies. Through analytical processes, fidelity in the wafer shapes to the “as intended” shapes ultimately achieve a better correction of the mask shapes. An increase in yield at chip manufacturing is a direct consequence for achieving this accuracy.
A significant difficulty when taking into consideration long range effects, such as flare, is the extent of the corrections flare effects required on the mask. In the prior art, optical lens aberrations are modeled by just the 37 lowest order Zernikes and, therefore, only aberrations that deviate light by 1 micron or less are included. The effect of aberrations dies off within that range. The flare effect, on the other hand, extends up to a few mms, thus covering the entire chip area. Current Model-Based OPC (MBOPC) software tools are not equipped to handle such long distance effects.
The limitations of the current methodology are shown in FIG. 3a. Therein are illustrated the extent of the flare kernel and the power spectral density of the flare accounting for the optical energy falling on the exposed mask. These are plotted against the logarithmic distance from the mask opening. The distance is measured in terms of the number of wave cycles/pupil or the distance x/(λ/2 NA), wherein λ is the wavelength of the light and NA, the numerical aperture. The limitations of the current art which are modeled by the 37 Zernike polynomial parameters Z1 through Z37 are shown in 301. On the other hand, the actual extent of the flare is shown in 304. The flare can be modeled by the Power Law F(x)=K/(x−x′)γ, wherein the constant γ ranges from 1 to 3, and depends on the optical system used in the lithographic process. The non-optimal interferometers that are used to measure the extent of flare is shown in 302. The non-optimal interferometer grossly underestimates the energy of the flare. On the other hand, a regular interferometer can be used to find the extent of the flare, as shown in 303. The variation of flare with respect to distance is shown in FIGS. 3b and 3c that illustrate variations of flare across field position.
In current MBOPC tools, interaction regions are of the order of 1 micron. Any increase in size of that region significantly affects the timing and accuracy of the simulation and, consequently, affects the OPC results. As a result, the need for fast and accurate flare modeling is being felt throughout the industry.
It has been shown through experimental data that the effect of flare on the variation of the Critical Dimension (CD) of transistors and other circuit devices can be as high as 6% of the designed dimensions for certain optical lithography process configurations. Therefore, it is imperative that these effects be considered in the simulation tools used by the MBOPC software.
The experimental justification of flare is shown in FIG. 4. Therein, the same mask structure printed on several locations on the wafer is shown having three different neighborhood background transmissions. Measured CDs of different wafer site locations are plotted against different background transmissions. CDs with 6%, 50% and 100% neighborhood background transmissions are shown in 401, 402 and 403, respectively. It is observed that the CD having a 6% neighborhood background transmission shows more pronounced CD variations than the other plots.
In the prior art, the following mathematical treatment in the optical proximity correction engine is commonly used. These approaches are in one form or another, related to the Sum of Coherent System (SOCS) method, which is an algorithm for efficient calculation of the bilinear transform.
Sum of Coherent Systems (SOCS) Method
The image intensity is given by the partially coherent Hopkin's equation (a bilinear transform):I0({right arrow over (r)})=∫∫∫∫d{right arrow over (r)}′dr″h({right arrow over (r)}−{right arrow over (r)}′)h*({right arrow over (r)}−r″)j({right arrow over (r)}′−r″)m({right arrow over (r)}′)m*({right arrow over (r)}″),where,                h is the lens point spread function (PSF);        j is the coherence;        m is the mask; and        IO is the aerial image.        
By using the SOCS technique, an optimal nth order coherent approximation to the partially coherent Hopkin's equation can be expressed as
            I      0        ⁡          (              r        ->            )        ≅            ∑              k        =        1            n        ⁢                  λ        k            ⁢                                                            (                              m                ⊗                                  ϕ                  k                                            )                        ⁢                          (              x              )                                                2            where λk, φk({right arrow over (r)}) represent the eigenvalues and eigenvectors derived from the Mercer expansion of:
            W      ⁡              (                                            r              ->                        ′                    ,                      r            ″                          )              =                            h          ⁡                      (                                          r                ->                            ′                        )                          ⁢        h        *                  (                      r            ″                    )                ⁢                  j          ⁡                      (                                                            r                  ->                                ′                            -                              r                ″                                      )                              =                        ∑                      k            =            1                    ∞                ⁢                              λ            k                    ⁢                                    ϕ              k                        ⁡                          (                                                r                  ->                                ′                            )                                ⁢                                    ϕ              k                        ⁡                          (                                                r                  ->                                ″                            )                                            ,suggesting that a partially coherent imaging problem can be optimally approximated by a finite summation of coherent imaging, such as linear convolution.SOCS with Pupil Phase Error
The above calculation assumes an ideal imaging system. However, when a lens aberration is present, such as the pupil phase error and apodization, one must include the pupil function:h({right arrow over (r)})=∫∫P({right arrow over (σ)})exp(i W({right arrow over (σ)}))exp(i2π{right arrow over (r)}·{right arrow over (σ)})d2{right arrow over (σ)}where,                P({right arrow over (σ)}) is the pupil transmission function; and        W({right arrow over (σ)}) is the pupil phase function, which contains both aberration and flare information.        
Because of the possible higher spatial frequency in the wavefront function, h({right arrow over (r)}) will have a larger spatial extent. In this case, the number of eigenvalues and eigenvectors required are higher than those of an ideal system. Hence, the kernel support area is extended to take account of the contribution from a distance greater than λ/NA. However, the basic mathematical structure and algorithm remains the same.
Physical Model of Flare
Flare is generally considered to be the undesired image component generated by high frequency phase “ripples” in the wavefront corresponding to the optical process. Flare thus arises when light is forward scattered by appreciable angles due to phase irregularities in the lens. (An additional component of flare arises from a two-fold process of backscatter followed by re-scatter in the forward direction, as will be discussed hereinafter). High frequency wavefront irregularities are often neglected for three reasons. First, the wavefront data is sometimes taken with a low-resolution interferometer. Moreover, it may be reconstructed using an algorithm at an even lower resolution. Second, even when the power spectrum of the wavefront is known or inferred, it is not possible to include the effect of high frequency wavefront components on an image integral that is truncated at a short ROI distance, causing most of the scattered light to be neglected. Finally, it is not straightforward to include these terms in the calculated image. The present invention addresses these problems.
Flare also arises from multiple reflections between the surfaces of the lens elements (including stray reflections from the mask and wafer). The extra path length followed by this kind of stray light usually exceeds the coherence length of the source. As a result, ordinary interferometric instruments will not detect it. Thus, as with wavefront ripple, flare from multiple reflections is not considered in the prior art OPC. The reasons are similar, i.e., stray reflections require extra effort to detect, they are largely generated outside ROI, and their contribution to the image is not handled by conventional algorithms of lithographic image simulation.
Stray reflections are dim, and generally represent an acceptable loss of image intensity. Thus, stray reflections are not particularly deleterious unless they actually illuminate the wafer with stray light. For this to occur, it is usually necessary for two surfaces to participate in the stray light path, one surface to back reflect a small portion of the primary imaging beam, and another to redirect some of the stray reflection forward towards the wafer. In nearly all cases, this light is strongly out of focus, and amounts to a pure background. In contrast, stray image light which is reflected back from the wafer and then forwarded from the underside of the mask remains reasonably well imaged at the wafer itself. For this reason, light in the primary image which is back reflected along this particular path (wafer to mask, and back to the wafer) is usually not counted as stray light (particularly if, as is usually the case, the twice-through beam is weak compared to the direct image). In contrast, light following other stray paths will form a defocused background at the wafer. Such an unpatterned background has a non-negligible impact even at a 1% level.
Nowadays, the reflectivity of the mask and wafer are held well below 100% (typically, an order of magnitude lower), but residual mask and wafer reflectivity are themselves typically an order of magnitude larger than the residual reflectivities of the lens element surfaces (which is highly transmissive). Nonetheless, the cumulative impact of all stray reflection paths which involve two successive stray reflections from lens surfaces are roughly comparable to the cumulative impact of those paths involving only a single lens reflection (together with a single reflection from the mask or wafer). This heightened cumulative impact is simply the result of the large number of lens surfaces (e.g., about 50) that are present in state of the art lithography lenses.
In principle, stray reflections do the most damage if focused or almost focused at the primary image plane, but in practice, this instance (unlikely to begin with) is checked for and avoided by lens designers. Stray reflections thus tend to be defocused for large distances, i.e., distances corresponding to the macroscopic scale of characteristic lens dimensions. As a result, the flare kernel from stray reflections is significantly flat on the scale of lens resolution, or even on the scale of typical flare measurement patterns. This behavior allows the contributions to the flare kernel from stray reflections and wavefront ripple to be distinguished from one another, since the latter falls off quite rapidly at distances larger than the lens resolution, e.g., as the inverse second or third power of distance, while the former falls off only slowly.
This is illustrated by the measurements shown in FIG. 3b, which plots an integrated flare within the total flare kernel of the lithographic lens, as measured by integrating boxes of various sizes. The integrated flare increases rapidly at short distance scales, e.g., far more rapidly within the first 10 microns than it does over the next 100 microns. This rapid variation is the result of a rapidly falling power-law flare component from wavefront ripple. In addition, stray reflections make a comparable contribution to total flare in the lens. However, the contribution of the stray reflection is effectively constant over approximately 500 μm scale of the measurement site.
Another characteristic of flare from stray reflections is that the flare kernel varies across the field, as illustrated in FIG. 3c. At both ends of the scatter distance scales that are plotted (integrated scatter outside 10 microns, and integrated scatter outside 80 microns), the amount of light in the flare kernel varies by roughly a factor of two across the field.
It is generally observed that the flare energy from a wavefront ripple follows approximately the inverse power law relationship given by: F(x)=K/(x−x′)γ. This is shown in FIG. 5. Therein, the extent of flare is plotted for a typical optical process of a numerical aperture (NA) of 0.75 and a pupil size (σ) of 0.3. Under this condition, the power law shows γ=1.85.
Currently there are no tools available for Model-Based Optical Proximity Correction (MBOPC) incorporating flare effects and there are no known patents or publications available to that effect. The present invention satisfies the need for a fast MBOPC which accurately incorporates the effect of flare.